There are two temperature sensors on our 'stangs. The Coolant Temperature Sensor senses the temp of the coolant coming into the engine, and that value is sent to the computer. The other is the Coolant Temperature Sending Unit, and it senses the temp of the coolant exiting the engine and sends it to the temp guage in the dash. The sensors are exclusive - the computer only reads the CTS, and the guage only reports the CTSU. You could be having trouble with one or both of the guages.
Here's a link to both sensors:
http://secure.50resto.com/category.cfm?SID=1&Category_ID=586
I was having a nasty overheating problem, much like what you described. My mechanic swore that my CTSU was bad, so the guage was falsely reporting an overheating problem. I got to the "A" several times, before I finally said enough, and made the mechanic check the rest of the system.
Turns out my CTS was bad - it was reporting temp values all over the place, from "cold" to "overheating" to "normal", etc. The computer didn't know what the temperature was, so it never turned the fan on. So, I WAS actually close to overheating!
I would think that an OBD I code reader would report the coolant temperature, so you may want to try there.
If you do replace one or both, I'd stick with Motorcraft. Most of the aftermarker sensors are made of plastic, but the Motorcraft ones are made of metal - brass, I think. The metal conducts the heat better, and it lasts longer.